Neither! We describe the “business” as if it is a single entity. The “business” is a collection of departments whose priorities and objectives frequently conflict. The functions of a PMO are best assigned to a corporate entity which spans the business departments and IT and is closely aligned with the overall business strategy.
The PMO should have oversight responsibilities for the entire life cycle of all projects (including non-IT). This will provide the best chance of addressing conflicting priorities, standarding across the enterprise, and aligning with the “business” objectives.